| Nome: | Descrição: | Tamanho: | Formato: | |
|---|---|---|---|---|
| In this study we propose a meshfree scheme for the numerical solution of boundary value problems (BVP) for the nonhomogeneous Cauchy-Navier equations of elastodynamics. The method uses the classical approach where first a particular solution for the partial differential equation (PDE) is calculated and then the corresponding homogeneous BVP is solved for the homogeneous part of the total solution. In particular, we approximate each component of the source term of the nonho-mogeneous PDE by superposition of plane wave functions with different frequencies and directions of propagation. Using these expansions, a particular solution for the PDE is derived in the form of a linear combination of elastic P-And S-waves, at no extra computational cost. In the second step of the scheme, we solve the corresponding homogeneous BVP using the classical method of fundamental solutions (MFS), with shape functions given by the Kupradze tensor. The accuracy and the convergence of the proposed technique is illustrated for a Dirichlet BVP, posed in a 2D multiply connected domain, bounded by polygonal and parametric curves. | 467.82 KB | Adobe PDF |
Orientador(es)
Resumo(s)
In this study we propose a meshfree scheme for the numerical solution of boundary value problems (BVP) for the nonhomogeneous Cauchy-Navier equations of elastodynamics. The method uses the classical approach where first a particular solution for the partial differential equation (PDE) is calculated and then the corresponding homogeneous BVP is solved for the homogeneous part of the total solution. In particular, we approximate each component of the source term of the nonho-mogeneous PDE by superposition of plane wave functions with different frequencies and directions of propagation. Using these expansions, a particular solution for the PDE is derived in the form of a linear combination of elastic P-And S-waves, at no extra computational cost. In the second step of the scheme, we solve the corresponding homogeneous BVP using the classical method of fundamental solutions (MFS), with shape functions given by the Kupradze tensor. The accuracy and the convergence of the proposed technique is illustrated for a Dirichlet BVP, posed in a 2D multiply connected domain, bounded by polygonal and parametric curves.
Descrição
Conference date - 10 November 2021 - 12 November 2021; Conference code - 175477
EISBN - 978-1-6654-3981-7
Link de acesso para o documento - https://scholar.google.com/scholar?q=Meshfree%20Approximate%20Solution%20of%20the%20Cauchy%E2%80%93%20Navier%20Equations%20of%20Elastodynamics
EISBN - 978-1-6654-3981-7
Link de acesso para o documento - https://scholar.google.com/scholar?q=Meshfree%20Approximate%20Solution%20of%20the%20Cauchy%E2%80%93%20Navier%20Equations%20of%20Elastodynamics
Palavras-chave
meshfree method plane wave functions method of fundamental solutions Cauchy-Navier equations of elastodynamics nonhomogeneous PDE
Contexto Educativo
Citação
S. S. Valtchev and N. F. M. Martins, "Meshfree Approximate Solution of the Cauchy– Navier Equations of Elastodynamics," 2021 3rd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA), Lipetsk, Russian Federation, 2021, pp. 149-154, doi: 10.1109/SUMMA53307.2021.9632193.
Editora
IEEE Canada
Licença CC
Sem licença CC